1. Field of the Disclosure
The present disclosure relates to neural networks; for example computer-implemented, as well as to methods for programming such networks. In particular, the present disclosure relates to a fault tolerant neural network capable of learning arbitrary multiple transformations, and a method of programming said neural network.
2. Background
Sensory perception and action are interdependent. In humans and other species, a behavior may be triggered by an ongoing situation and reflects a being's immediate environmental conditions. This type of behavior is often referred to as stimulus-response reflexes. The interdependency between stimulus and response creates an action perception cycle in which a novel stimulus triggers actions that lead to a better perception of itself or its immediate environmental condition and the cycle continues.
Human behavior is much more flexible than exclusive control by stimulus-response cycles. One attribute of intelligent-based systems is the ability to learn new relations between environmental conditions and appropriate behavior during action perception cycles. The primary mode of communication between neurons in the brain is encoded in the form of impulses, action potentials or spikes. The brain is composed of billions of neural cells, which are noisy, imprecise and unreliable analog devices. The neurons are complex adaptive structures that make connections between each other via synapses. A synapse has a presynaptic portion, comprising the axon of a neuron, inputing a spike into the synapse, and a postsynaptic portion comprising the dendrite of a neuron, sensitive to the spike being received in the synapse. The synapses may change their function dramatically depending upon the spiking activity of the neurons on either side of the synapse. The synapse includes an adaptation mechanism that adjusts the weight, or gain, of the synapse according to a spike timing dependent plasticity (STDP) learning rule.
Under the STDP rule, if an input spike to a neuron tends, on average, to occur immediately before that neuron's output spike, then that particular input is made somewhat stronger. On another hand, if an input spike tends, on average, to occur immediately after an output spike, then that particular input is made somewhat weaker hence: “spike-timing-dependent plasticity”. Thus, inputs that might be the cause of the post-synaptic neuron's excitation are made even more likely to contribute in the future, whereas inputs that are not the cause of the post-synaptic spike are made less likely to contribute in the future. The process continues until a subset of the initial set of connections remains, while the influence of all others is reduced to 0. Since a neuron produces an output spike when many of its inputs occur within a brief period the subset of inputs that remain are those that tended to be correlated in time. In addition, since the inputs that occur before the output are strengthened, the inputs that provide the earliest indication of correlation eventually become the final input to the neuron.
Brain architectures composed of assemblies of interacting neurons and synapses with STDP can solve complex tasks and exhibit complex behaviors in real-time and with high precision but with very low power. However, modeling such activity in a physical network is complex.
Neural networks using analog and digital circuitry and computer-implemented methods have been discussed to implement a STDP learning rule. However, current models do not have the capacity to be tolerant to faults (i.e., to partial absence of sensory or motor input signals) introduced either from the beginning of the learning process or after some initial learning has taken place. Accordingly, the known systems that implement a STDP learning rule are incapable of learning for example arbitrary multiple transformations in a fault tolerant fashion.
Several examples of communication systems that have experienced the above described communication issues include T. P. Vogels, K. Rajan and L. F. Abbott, “Neural Network Dynamics,” Annual Review Neuroscience, vol. 28, pp. 357-376, 2005; W. Gerstner and W. Kistler, Spiking Neuron Models—Single Neurons, Populations, Plasticity, Cambridge University Press, 2002; H. Markram, J. Lubke, M. Frotscher, & B. Sakmann, “Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs,” Science, vol. 275, pp. 213-215, 1997; Bi, G. Q., & M. Poo, “Activity-induced synaptic modifications in hippocampal culture: dependence on spike timing, synaptic strength and cell type,” J. Neuroscience. vol. 18, pp. 10464-10472, 1998; J. C. Magee and D. Johnston, “A synaptically controlled, associative signal for Hebbian plasticity in hippocampal neurons,” Science vol. 275, pp. 209-213, 1997; S. Song, K. D. Miller and L. F. Abbott, “Competitive Hebbian Learning Through Spike-Timing Dependent Synaptic Plasticity,” Nature Neuroscience, vol. 3 pp. 919-926, 2000; A. P. Davison and Y. Fregnac, “Learning Cross-Modal Spatial Transformations through Spike-Timing Dependent Plasticity,” Journal of Neuroscience, vol. 26, no. 2, pp. 5604-5615, 2006; Q. X. Wu, T. M. McGinnity, L. P. Maguire, A. Belatreche, B. Glackin, “2D co-ordinate transformation based on a spike-timing dependent plasticity learning mechanism,” Neural Networks, vol. 21, pp. 1318-1327, 2008; Q. X. Wu, T. M. McGinnity, L. P. Maguire, A. Belatreche, B. Glackin; “Processing visual stimuli using hierarchical spiking neural networks,” International Journal of Neurocomputing, vol. 71, no. 10, pp. 2055-2068, 2008. Each of the above references is hereby incorporated by reference in its entirety.
FIG. 1 illustrates a network model described in the above reference entitled “Learning Cross-Modal Spatial Transformations through Spike-Timing Dependent Plasticity”. FIG. 1 shows a neural network that receives in input the angle θ at the joint of an arm with 1 Degree of Freedom (df) and the position x of the end of the arm, in a vision-centered frame of reference. After a learning phase the neural network becomes capable of outputting x based on the angle θ at the joint. The neural network 10 comprises a first one-dimension array 12 of input neurons 14 that each generate spikes having a firing rate that increases as a function of the angle θ getting closer to an angle assigned to the neuron. FIG. 1 illustrates the firing rate FR of all the neurons 14 of array 12 for a given value of the angle θ. The neural network 10 further comprises a second one-dimension array 16 of input neurons 18 that each generate spikes having a firing rate that increases as a function of the position x getting closer to a predetermined value assigned to the neuron. FIG. 1 illustrates the firing rate FR of all the neurons 18 of array 16 for a given value of the position x. The neural network 10 comprises a third one-dimension array 20 of neurons 22.
Connections are initially all-to-all (full connection) from the neurons 14 to the neurons 22, and the strength of the connections is subject to modification by STDP. Connections from the neurons 18 to the neurons 22 are one to one. The strength of these non-STPD (or non-plastic) connections is fixed.
After a learning phase where stimuli corresponding to random angle θ and their equivalent position x are sent to array 20, array 16 ceases to provide input to the array 20, and array 20 outputs a position x in response to a based on the angle θ at the joint. FIG. 1 illustrates the firing rate FR output by the neurons 22 of array 20 in response to a given value of the angle θ after the learning phase.
FIG. 2 illustrates in schematic form the neural network 10 of FIG. 1 and shows input array/layer 12 fully connected to output array/layer 20 and training array/layer 16 connected on-to-one to output array/layer 20.
FIG. 3 schematizes a neural network 30 such as disclosed in the Wu et al. reference above. The neural network 30 comprises a training layer 16 connected one-to-one to an output layer 20 as detailed in FIG. 1. Further, neural network 30 comprises two input layers 12 topographically connected in input of a network layer 32, the network layer 32 being fully connected in input of output layer 20. As outlined above, the neural networks of FIGS. 1-3 are not tolerant to faults such as a partial absence of sensory or motor input signals, introduced either from the beginning of the learning process or after some initial learning has taken place.
There exists a need for neural networks that would be tolerant to fault.